Question

A boat covers 50km upstream and 40km downstream in total 7.5 hours.The speed of boat in still water is 15km/hr.If the speed of stream is xkm/hr then which of the following quadratiic equations correctly represents this case?​

Answer 1

Answer:

Let x be the speed of the stream.

⇒ Speed of the boat in still water is 8km/hr

⇒ The speed of the boat in upstream is 8−xkm/hr

⇒ The speed of the boat in downstream is 8+xkm/hr

⇒ The time taken by the boat to cover 15km=

8−x

15

hr

⇒ The time taken by the boat to cover 22km=

8+x

22

hr

According to the question,

⇒

8−x

15

+

8+x

22

=5

⇒ 15(8+x)+22(8−x)=5(8−x)(8+x)

⇒ 120+15x+176−22x=5(64−x

2

)

⇒ 296−7x=320−5x

2

⇒ 5x

2

−7x−24=0

⇒ 5x

2

−15x+8x−24=0

⇒ 5x(x−3)+8(x−3)=0

⇒ (x−3)(5x+8)=0

⇒ x−3=0 and 5x+8=0

⇒ x=3 and x=−

5

8

Speed cannot be negative.

∴ The speed of the stream is 3km/hr